The company disclosed on Friday that an internal research version of Claude identified the parameters as outputs from a conventional C programming language pseudorandom number generator, initialised using Unix timestamps. Anthropic said the investigation took less than 30 minutes and uncovered no vulnerability requiring changes to existing security systems.
The findings concern five elliptic curves designated P-192, P-224, P-256, P-384 and P-521, included in standards issued by the US National Institute of Standards and Technology. Their unexplained numerical starting values, known as seeds, had prompted questions about whether the curves could contain deliberately concealed weaknesses.
Anthropic’s researchers identified the generator as lrand48, a software function that produces predictable sequences from an initial value. They found that timestamps corresponding to the late 1990s could reproduce published seeds, offering a testable explanation for numbers whose original selection process had never been documented publicly.
The distinction matters because the seeds help determine mathematical parameters used by the Elliptic Curve Digital Signature Algorithm, or ECDSA. That technology enables systems to authenticate digital signatures and verify that electronic messages, software and transactions have not been altered.
Anthropic stressed that its discovery did not constitute a cryptographic attack. Although lrand48 is unsuitable for generating secret cryptographic keys, reconstructing these public curve parameters does not expose private keys or undermine signatures generated using the standard.
The company said the reproducible procedure made deliberate manipulation of the published curves less plausible. However, it acknowledged that the investigation had not established every decision taken by their original designers, including why some mathematically acceptable candidates were bypassed.
For the widely deployed P-256 curve, the researchers reconstructed a sequence in which the published seed emerged as the 1,842nd candidate. The software generated successive 20-byte values from a timestamp-initialised sequence until reaching the value incorporated into the standard.
The inquiry began when an Anthropic employee asked an internal research model to investigate the seeds without directing it towards an established theory involving a secret phrase. Earlier attempts by company staff to pursue that explanation had failed.
Claude instead examined the characteristics of software random-number generators available when the parameters were created. The research team published code allowing others to reproduce its calculations, making the central technical finding independently testable.
Cryptographer Filippo Valsorda confirmed that the researchers had claimed a longstanding public bounty for identifying the seeds. He said the claim arrived on 15 October and that the reward, increased to $36,864 for charitable donation, would go to the Internet Security Research Group, which operates the Let’s Encrypt certificate authority.
The unexplained origins had attracted scrutiny because the NSA supplied the seeds without a public account of their derivation when NIST adopted the relevant digital signature standard in 2000. The lack of transparency left room for suspicions even though the curves remained widely trusted by specialists.
One earlier account came from former NSA cryptographer Jerry Solinas, who suggested that a humorous phrase might have been hashed to produce the numbers. Solinas, who died in 2023, had acknowledged uncertainty about the details. Anthropic’s reconstruction points to a different process.
The researchers also identified origins for additional standardised curve seeds, but their findings did not settle every associated question. Anthropic said the seed for the binary curve B-163 remained unexplained, while the selection of base points for P-224, P-256, P-384 and P-521 could not be reconstructed using the same method.
The investigation distinguished the process of choosing a seed from the subsequent mathematical calculation that turns it into a curve parameter. The published seeds were processed using a hash function under the standard, but Anthropic found that the seeds themselves originated from generator output rather than from hashing a remembered sentence. This distinction helped explain why earlier searches based on supposed phrases had yielded nothing, while comparisons against historical software routines produced matching numerical sequences.
Base points are separate published mathematical values used in elliptic-curve operations. Anthropic said its investigation had explained some other base points, but the outstanding cases required different evidence. The company also noted that several viable candidate curves appeared to have been skipped during generation, without an established reason for those omissions.
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